The given expression is:

\[
x + 5\sqrt{27x^3} + 0x^2 + 0x + 8
\]

We can simplify this step by step:

1. The term \(0x^2 + 0x\) is zero, so we can eliminate these terms.
2. We simplify the square root term: \(\sqrt{27x^3}\).

\[
\sqrt{27x^3} = \sqrt{9 \cdot 3x^3} = \sqrt{9} \cdot \sqrt{3x^3} = 3\sqrt{3x^3}
\]

Thus, \(5\sqrt{27x^3} = 5 \cdot 3\sqrt{3x^3} = 15\sqrt{3x^3}\).

Now, the simplified expression is:

\[
x + 15\sqrt{3x^3} + 8
\]

This is the final simplified form of the given expression.

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Would you like further clarification on any step? 

Here are some related questions:

1. How do you simplify expressions involving square roots and exponents?
2. What is the rule for simplifying terms like \(\sqrt{a^b}\)?
3. Can we solve this expression for any particular value of \(x\)?
4. How can we apply these simplifications in solving equations?
5. How do square roots affect terms with variables raised to powers?

**Tip:** When simplifying square roots, break down the radicand (the number inside the root) into prime factors for easier simplification.

Learn how to simplify the algebraic expression x + 5√27x³ + 8 by eliminating zero terms and simplifying square roots. This problem is ideal for students in Grades 8-10, covering key concepts like square roots and algebraic simplification.

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